The exchange you are using will obviously know all the addresses that you withdraw coins to. You won't have any immediate privacy against them, whether or not you reuse addresses.
However, if you reuse the same address, then in the future when you want to spend those coins, whoever you send them to will be able to see all of your past transactions to that address, including your past, present, and future balance. On the other hand, if you used a new address for every withdrawal, then whoever you send coins to in the future would only be aware of some subset of your addresses (ie, the UTXOs that were used to make the payment, and no more).
Think of it like this: when you pay for a $26 lunch with $30 cash and ask for change, then the waiter will know you have at least $4 left. If you paid for a $26 lunch with your entire account balance of $12,000 and asked for change, well then the waiter will know that you have at least $11,974 left. Obviously, there is no reason to give the waiter that information. When using bitcoin, you can protect this information by not reusing addresses.
Further, if you send some coins from your re-used address to the publicly-known address of some service/person/etc, then everyone else you transact with will be able to see that you transacted with said publicly-known service/person/etc. This hurts your privacy, but also potentially the privacy of others you are transacting with.
If you really must use one address to receive DCA funds from an exchange, you could perhaps make a habit of transferring those funds into another wallet from time to time, using a new address for each new transfer. Each transaction you make adds some plausible deniability to the history of funds, so while this technique is very far from a perfect privacy fix that will thwart a well-provisioned blockchain spy, you could at least use it overcome the most basic of privacy-eroding analysis.